Finite Group Databasebeta

← #18081512

Subgroups — #18081512

Order 4864.

720 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10597320C211yesmaximal, characteristic
2#14563488C211yesmaximal, characteristic, complemented
3C2×#11926273C214yesmaximal, complemented
4C4×C19×C4⋊C8C211yesmaximal, characteristic, complemented
5C2×#10597320C411yescharacteristic
6C2×C4×D76—21no—
7C2×C4×D76—21no—
8C2×C4×D76C2212yes—
9C2×C4⋊(C19⋊C8)C2212yes—
10C2×#10597260—21no—
11#11926446—21no—
12#11926446—21no—
13#11926446C412yes—
14#11926414C411yescharacteristic
15#11926299—21no—
16#11926273—28no—
17C2×C19×C4⋊C8—21no—
18C2×C4×C8×C19C2212yes—
19C43×C19C2211yescharacteristic
20C19×#336—21no—
21C22×D76—21no—
22C22×D76—21no—
23C22×D76C2×C412yes—
24C22×C4×D19—22no—
25C22×C8×C19—22no—
26C2×C42×C19C2×C411yescharacteristic
27C2×C42×C19C2×C411yescharacteristic
28C2×C42×C19D411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33C2×(C2×D19)⋊C4—22no—
34C2×(C2×D19)⋊C4—22no—
35C2×(C2×D19)⋊C4—22no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19C2×C412yes—
39C22×C19⋊C8—22no—
40#10597320—24no—
41C4×D76—24no—
42C4×D76—24no—
43C4×D76—44no—
44C4×D76—42no—
45C4×D76—42no—
46C19×C4⋊C8—24no—
47C4×C8×C19—24no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)D414yescomplemented
50#10597260—42no—
51C23×D19—22no—
52C22×C4×C19C22⋊C411yescharacteristic
53C22×C4×C19C22⋊C411yescharacteristic
54C22×C4×C19C22⋊C411yescharacteristic
55C22×C4×C19C22⋊C411yescharacteristic
56C22×C4×C19C22×C411yescharacteristic
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×Dic19—22no—
60C2×D76—24no—
61C2×D76—24no—
62C2×D76—24no—
63C2×D76—24no—
64C2×D76—22no—
65C2×D76—42no—
66C2×D76—42no—
67C2×D76—42no—
68C2×D76—42no—
69C2×D76M1614yes—
70C2×C4×D19—44no—
71C2×C4×D19—42no—
72C2×C4×D19—42no—
73C2×C4×D19—44no—
74C2×C8×C19—24no—
75C2×C8×C19—42no—
76C2×C8×C19—42no—
77C42×C19—22no—
78C42×C19—22no—
79C42×C19—22no—
80C42×C19—22no—
81C42×C19—41no—
82C42×C19D812yes—
83C42×C19SD1612yes—
84C42×C19C2×D412yes—
85C42×C19#4112yes—
86(C2×D19)⋊C4—44no—
87(C2×D19)⋊C4—44no—
88(C2×D19)⋊C4—42no—
89(C2×D19)⋊C4—42no—
90C4⋊Dic19—24no—
91C4⋊Dic19—42no—
92C4⋊Dic19—42no—
93C2×C19⋊C8—24no—
94C2×C19⋊C8—42no—
95C2×C19⋊C8—42no—
96#9678—191nomaximal, Sylow
97C23×C19C2×C22⋊C411yescharacteristic
98C22×D19—24no—
99C22×D19—42no—
100C22×D19—42no—
101C22×D19—42no—
102C22×D19—42no—
103C22×D19—42no—
104C22×D19—42no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19#10212yes—
117C2×C4×C19#10212yes—
118C2×C4×C19#10412yes—
119C2×C4×C19C4×D412yes—
120C2×C4×C19#12112yes—
121C2×C4×C19#12411yescharacteristic
122C2×C4×C19#12711yescharacteristic
123C2×C4×C19C2×M1612yes—
124C2×C4×C19#13112yes—
125C2×C4×C19C2×D811yescharacteristic
126C2×C4×C19C2×SD1611yescharacteristic
127C2×C4×C19AGL(1,ℤ/8)12yes—
128C2×Dic19—42no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131D76—28no—
132D76—48no—
133D76—48no—
134D76—44no—
135C4×D19—84no—
136C4×D19—84no—
137C8×C19—44no—
138C19⋊C8—44no—
139C4×#127—191no—
140#1767—191no—
141C4×C4⋊C8D1911yescharacteristic, complemented
142C2×D4⋊C8—194no—
143C22×C19#39011yescharacteristic
144C22×C19#40711yescharacteristic
145C22×C19#40811yescharacteristic
146C22×C19C2×#10211yescharacteristic
147C22×C19#41811yescharacteristic
148C22×C19C2×#10411yescharacteristic
149C22×C19#42111yescharacteristic
150C2×D19—44no—
151C2×D19—44no—
152C2×D19—44no—
153C2×D19—82no—
154C2×D19—82no—
155C2×D19—82no—
156C2×D19—82no—
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—22no—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—41no—
163C4×C19#43514yes—
164C4×C19#45912yes—
165C4×C19#46012yes—
166Dic19—82no—
167C2×#127—191no—
168C2×C4×D4—192no—
169C2×C4×D4—381no—
170C2×C4×D4—381no—
171C2×C4⋊C8—21no—
172C2×C4⋊C8—192no—
173C2×#97—381no—
174C2×C4×C8C2×D1912yes—
175#390—192no—
176#390—381no—
177#390—381no—
178#384—191no—
179C43C2×D1911yescharacteristic
180#336—21no—
181#336—381no—
182D4⋊C8—388no—
183C2×C19#148611yescharacteristic
184C2×C19#149011yescharacteristic
185C2×C19#149211yescharacteristic
186C2×C19#149611yescharacteristic
187C2×C19#195511yescharacteristic
188C2×C19#198011yescharacteristic
189C2×C19#198211yescharacteristic
190D19—84no—
191C22×D4—192no—
192C22×D4—381no—
193C22×D4—381no—
194C23×C4—382no—
195C22×C8—22no—
196C22×C8—382no—
197#127—384no—
198C4×D4—384no—
199C4×D4—384no—
200C4×D4—764no—
201C4×D4—762no—
202C4×D4—762no—
203C2×C4⋊C4—192no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—381no—
206C2×C22⋊C4—382no—
207C2×C22⋊C4—382no—
208C2×C22⋊C4—382no—
209C2×C42C4×D1911yescharacteristic
210C2×C42C4×D1911yescharacteristic
211C2×C42D7611yescharacteristic
212C2×C42D7611yescharacteristic
213C2×C42C22⋊D1911yescharacteristic
214C2×C42C22⋊D1911yescharacteristic
215C2×C42C22×D1911yescharacteristic
216C4⋊C8—24no—
217C4⋊C8—194no—
218C4⋊C8—382no—
219#97—762no—
220C4×C8—24no—
221C19#967811yescharacteristic, complemented, Sylow
222C24—382no—
223C2×D4—194no—
224C2×D4—384no—
225C2×D4—384no—
226C2×D4—384no—
227C2×D4—384no—
228C2×D4—382no—
229C2×D4—762no—
230C2×D4—762no—
231C2×D4—762no—
232C2×D4—762no—
233C22×C4—382no—
234C22×C4—764no—
235C22×C4—762no—
236C22×C4—762no—
237C22×C4—764no—
238C22×C4(C2×D19)⋊C411yescharacteristic
239C22×C4(C2×D19)⋊C411yescharacteristic
240C22×C4(C2×D19)⋊C411yescharacteristic
241C22×C4(C2×D19)⋊C411yescharacteristic
242C22×C4C2×C4×D1911yescharacteristic
243C22×C4C2×D7611yescharacteristic
244C22×C4C2×C22⋊D1911yescharacteristic
245C2×C8—24no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—384no—
249C2×C8—762no—
250C2×C8—762no—
251C4⋊C4—384no—
252C4⋊C4—762no—
253C4⋊C4—762no—
254C22⋊C4—764no—
255C22⋊C4—762no—
256C22⋊C4—762no—
257C22⋊C4—764no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42#6451612yes—
264C42D15212yes—
265C42D4×D1912yes—
266C42#6454512yes—
267C23—384no—
268C23—762no—
269C23—762no—
270C23—762no—
271C23—762no—
272C23—762no—
273C23—762no—
274C23C2×(C2×D19)⋊C411yescharacteristic
275D4—388no—
276D4—768no—
277D4—768no—
278D4—764no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—762no—
291C2×C4—762no—
292C2×C4—762no—
293C2×C4—1524no—
294C2×C4—1524no—
295C2×C4#1059726212yes—
296C2×C4#1059727812yes—
297C2×C4#1059727812yes—
298C2×C4#1059733912yes—
299C2×C4#1059734112yes—
300C2×C4#1059734712yes—
301C2×C4C2×#6451611yescharacteristic
302C2×C4C2×D15211yescharacteristic
303C2×C4M16×D1912yes—
304C2×C4#1059735412yes—
305C2×C4#1059738611yescharacteristic
306C2×C4#1059739311yescharacteristic
307C8—44no—
308C8—764no—
309C22—764no—
310C22—764no—
311C22—764no—
312C22—1522no—
313C22—1522no—
314C22—1522no—
315C22—1522no—
316C22#1192644511yescharacteristic
317C22#1192650711yescharacteristic
318C22#1192651011yescharacteristic
319C22C2×#1059727811yescharacteristic
320C22#1192655011yescharacteristic
321C22C2×#1059726211yescharacteristic
322C22#1192656211yescharacteristic
323C4—22no—
324C4—22no—
325C4—22no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—1522no—
330C4#1192661414yes—
331C4#1192674012yes—
332C4#1192674512yes—
333C2—1524no—
334C2#1456206111yescharacteristic
335C2#1456207911yescharacteristic
336C2#1456208711yescharacteristic
337C2#1456210511yescharacteristic
338C2#1456443211yescharacteristic
339C2#1456455311yescharacteristic
340C2#1456456111yescharacteristic
subgroupG/H
centerC22×C4C2×D76
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×C4⋊C8C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597320C4
cosocleC2×C42×C19C23
hypercenterC4×C4⋊C8D19
hypocenterC19#9678
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14563488C2semidirect
3. C2×#11926273C2semidirect
4. C4×C19×C4⋊C8C2semidirect
49. C4⋊(C19⋊C8)D4semidirect
141. C4×C4⋊C8D19semidirect
221. C19#9678semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#105973202
#145634882
C2×#119262732
C4×C19×C4⋊C82
#967819